Madrigal,
Here's an analogy why high current is important (this has already been mentioned here before):
8 penlight batteries total to 12volts right? A car battery is also rated 12 volts right? Given the same voltage of 12, which between the two would you use to start your car? The penlight battery or the car battery? The latter of course. The reason, because it has more current!!!
Same with amplifiers, the more current, the more power output it can provide.
It is also important to note that not all power ratings disclosed by the manufacturers are based on the same methodology. For example, Harman/Kardon's power ratings are usually based on the entire frequency range of 20Hz-20kHz, while some Japanese brands power ratings are based only on the frequency range of 1Khz. So basically, you end up comparing apples to oranges.
Another very important aspect to know is that power ratings that are normally disclosed are based only on a specific resistance, usually 8 ohms. But in reality, speaker impedance flucutates invariably. The lower the impedance, the more current it requires of the amplifier. Therefore, the higher the current the amplifier can produce, the better.
This has already been discussed here in greater detail but it seems that the search engine is not functioning properly. So perhaps, you can ask the moderators to direct you to the appropriate threads.
Good luck.